%f (14) 



R 



where K, proportional to the mass of gas within the bubble, may depend upon 

 the temperature. At equilibrium, the bubble radius, R, is stationary, say 

 R = R . Then Equation (12) is 



2a 



o = - ( Pot -p v ) - r^ + 73 < 15 > 



o R 

 o 



Now we may ask whether or not this equilibrium is stable. To answer this 

 question we put, in the usual way, 



R = R (l+£(t)) (16) 



o 



where e(t) is supposed to be a small number, and linearize Equation (12) 

 to get 



.. *V£ , 1 /3K 2a s\ P co-Pv 2CT s + K 



R o pR o \ R o ° / ° PR o 



But, the right hand side is identically zero. We have now the equation of 

 a single degree of freedom oscillator and we expect that 



e = e jnt (18) 



o 



0, being the frequency. We readily find that 



n-2£L± A -^,v-v/p (19) 



R 2 V S R 4 



60 



